The main problem with quests is that the moment you  trigger them they do not update with the current game situation.

In this case I have a problem with the Broken Lords but it already happened with a different quest in Vaulter questline. 

I triggered the second Broken Lords quest, the one where you have to research 8 ERA I technologies. The problem is that I've already researched them and the game doesn't acknowledge it, which means I cannot progress.

The same problems occured with my Vaulter quests even though I don't remember specifics right now. But the cause is always the same: the game doesn't acknowledge your accomplishments achieved before a certain quest was triggered.

EDIT: Please disregard it, I was wrong, the game does acknowledge it. :(